1. Field of the Invention
The present invention relates to a method for detecting and correcting errors in error detection and correction codes which are used in PCM recording and reproducing of analog signal information such as music signals.
2. Description of the Related Art
Conventionally, error detection and correction codes have been used in order to detect and correct errors produced in recording and transferring pulse-code-modulated information. Particularly, in the case where a recording/transferring medium which may result in many errors, a plurality of error detection and correction codes have been used in a multiplexed manner such that error correction and detection is carried out using the respective codes, thereby enhancing the entire error detection and correction capability.
One such prior art is an error detection and correction method disclosed in "DIGITAL AUDIO TAPERECORDER SYSTEM (R-DAT) RECOMMENDED DESIGN STANDARD" issued Apr. 16, 1986 by the DAT Conference, which will be explained below
R-DAT (Rotationary Head Digital Audio Taperecorder) is a taperecorder for recording and reproducing a PCM audio signal on a magnetic tape using a rotationary head. In its mandatory mode, the two channel audio signals are recorded and reproduced with the quantizing bit number of 16 bits and at the sampling frequency of 48 KHz.
Generally, magnetic recording systems require stabilized contact between a head and a tape, but it is inevitable that a contact state is casually deteriorated due to flaws or dust on the tape. Thus, an error correction code is added to the PCM audio signal to make it possible to reproduce the PCM audio signal correctly, even if a recording/reproducing state of the PCM signal is deteriorated. R-DAT adopts the doubly-encoded Reed-Solomon code as this error correction code.
In R-DAT, an audio signal quantized in 16 bits is divided into two 8 bit data portions called "symbol", which include upper 8 bits and lower 8 bits, and thereafter the 8 bit data are encoded with the doubly-encoded Reed-Solomon code.
FIG. 1 shows an arrangement of the doubly-encoded Reed-Solomon code As seen from FIG. 1, one page of an error detection and correction code is constituted by lengthwise 32 symbols which constitute a first codeword called "C.sub.1 code" and breadthwise 32 symbols which constitute a second codeword called "C.sub.2 code". One page consists of 32 codewords of the C.sub.1 code and 32 codewords of the C.sub.2 code.
The C.sub.1 code is a Reed-Solomon code of (32, 28, 5) on a Galois field GF (2.sup.8) consisting of 28 data symbols and 4 parity symbols (the parity in the C.sub.1 code is referred to as P partiy). The C.sub.2 code is a Reed-Solomon code of (32, 26, 7) on a Galois field GF (2.sup.8) consisting of 26 data symbols and 6 parity symbols (the parity in the C.sub.2 code is referred to as Q parity). The minimum distance of the C.sub.1 code represents a minimum value of the Hamming distance between all different codewords in the C.sub.1 code; and the value of this minimum distance between codes is 5. Thus, error correction can be made up to 4 symbols, if the error locations are known, and, up to 2 symbols, if they are not known. The minimum distance of the C.sub.2 code is 7. Thus, error correction can be made up to 6 symbols, if the error locations are known, and, up to 3 symbols, if they are not known.
The occurrence pattern of errors can be roughly classified into a random error and a burst error The countermeasure for the burst error is critical for R-DAT The burst error means that errors successively occur due to the flaws or defects on the tape. When the burst. error occurs, data are lost in a concentrated location, so that it is difficult to correct or conceal (interpolating using the data before and after the erroneous data) the errors. Then, in order to disperse the burst error into several codewords so that the burst error is converted into a shorter burst error or a random error, a technique of interleaving in which the codewords are recorded in a dispersed manner is used.
FIG. 2 is a view showing a format of interleaving the error detection and correction codes of R-DAT, and it shows, as a whole, one track formed by helical scanning of the rotary head.
On an actual magnetic recording tape, one track is formed on the magnetic recording tape by sequentially recording 128 columns in total in such a way that a first leftmost column of the error detection and correction codes shown in FIG. 2 is recorded sequentially from top to bottom in the vertical direction, then a second column adjacent to the first column is recorded, and so on. One track is constituted by four pages each of which pages is represented by a shaded part in FIG. 2 and corresponds to the whole configuration of the error detection and correction code shown in FIG. 1. Therefore, one track is constituted by 128.times.32=4096 symbols The C.sub.1 code is interleaved in the vertical direction in the order of 31.fwdarw.30.fwdarw.29.fwdarw.. . . .fwdarw.0 at every other symbols which are adjacent to each other.
The C.sub.2 code is interleaved in the horizontal direction in the order of 31.fwdarw.30.fwdarw.29.fwdarw.. . . .fwdarw.0 at every four symbols extending over one entire track.
FIG. 3 shows the procedure of decoding in the conventional error detection and correction method for the error detection and correction codes constituted as mentioned above.
The decoding of the doubly-encoded codes is performed in two steps such that the first codewords are initially decoded to output flags representative of the decoding states and thereafter the second codewords are decoded on the basis of the flags representative of the first codewords to output the decoding states of the second codewords.
However, this conventional error detection and correction method has a disadvantage in that the quality of a reproduced signal is deteriorated when a burst error occurs, and particularly it is greatly deteriorated when the pulse noise (unusual sound) due to misdetection of an error is produced. For example, in the case where, in decoding the second codewords, erasure correction is to be carried out on the basis of the flags representative of the decoding states of the first codewords, if a condition of six erasures is satisfied, six erasure corrections are unconditionally carried out. Thus, if there is an error at a location other than the locations where six flags stand, misdetection of the error necessarily occurs, thus producing an unusual sound.